If σx is a permutation of the components of x and c(x) = (c, m) then c(σx) = (c, σm).
There is a floating point error in c proportional to 1/(product of components of argument).
c fails if any component of its argument is 0 but

lim(x→0)c OF c((x, y, … w, x)) = c OF c((x, y, … w)) and

lim(x→0)m OF c((x, y, … w, x)) = m OF c((x, y, … w)) with a c/2 appended to the vector.

Of the arguments to c we say that x and y are complementary if
1/Σx_{i} + 1/Σy_{i} = 1.
The cube slices produced by complementary arguments form complements to the cube if you reflect one of them about the center of the cube.
If x is an argument to c then ip(x) is the complementary argument.

From this equation:

m'^{j}
= _{∫} (x^{j} + d^{j})*dm*
= m^{j} + md^{j}

from here we conclude that the vector sum of the moment 1’s should be (½, ½, …).
Consider the test ts((3, 0.001)) and corresponding test.
That divides the square very nearly into .

centroid 1 m1/m0 centroid 2 (1, 1, …) - m1'/m0' Weighted mean at (½, ½, …) (m1/m0)m0 + ((1, 1, …) - m1'/m0')m0' = (½, ½, …) m1 + (m0', m0', …) - m1'

`sl` is the fraction of the vertical body diagonal above the water.

Code constructs beginning “(0=1 |” are code fragments that are turned off. Changing them to begin “(0=0 |” turns them on. Each is a test of sorts.

The three columns are:

- Cube density
- Height above water of highest point of body.
- Height of centroid of that part of body above water.